Lemma 2.5 (Lemma 4.4 in [1]}) 

Suppose \((M,g)\)  is a closed Riemannian surface,
and \(T\)  is a geodesic triangulation of \((M,g)\) , and \(l\in \mathbb {R}_{>0}^{E(T)}\)  denotes the geodesic lengths of the edges.
